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Recursive contracts in non-convex environments

Author

Listed:
  • Chengfeng Shen
  • Felix Kubler
  • Zhennan Zhou

Abstract

Many dynamic contracting problems in economics are non-convex, and deterministic optima can be dominated by randomized solutions. We develop a recursive method to compute optimal lotteries in the presence of forward-looking constraints, extending the approach of \cite{marcet2019recursive} to non-convex settings. We show that an inf-sup functional equation recovers the correct value when lotteries are conducted after agents commit to actions (``ex-ante'' lotteries), though the resulting solution often lacks economic meaning. Replacing the inf-sup with a sup-inf operator delivers the correct value of an economically more relevant ``ex-post'' lottery problem, where agents act after observing the lottery's outcome. We also develop an algorithm to recover the optimal lottery policies from the solution of the functional equation.

Suggested Citation

  • Chengfeng Shen & Felix Kubler & Zhennan Zhou, 2025. "Recursive contracts in non-convex environments," Papers 2511.20303, arXiv.org, revised Oct 2026.
    • Handle: RePEc:arx:papers:2511.20303
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    References listed on IDEAS

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    1. Gaetano Bloise & Paolo Siconolfi, 2022. "A Negishi Approach to Recursive Contracts," Econometrica, Econometric Society, vol. 90(6), pages 2821-2855, November.
    2. Thomas Cooley & Ramon Marimon & Vincenzo Quadrini, 2004. "Aggregate Consequences of Limited Contract Enforceability," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 817-847, August.
    3. Patrick J. Kehoe & Fabrizio Perri, 2002. "International Business Cycles with Endogenous Incomplete Markets," Econometrica, Econometric Society, vol. 70(3), pages 907-928, May.
    4. Edward Simpson Prescott, 1999. "A primer on moral-hazard models," Economic Quarterly, Federal Reserve Bank of Richmond, issue Win, pages 47-78.
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